The estimation of a random coefficient AR(1) process under moment conditions. (English) Zbl 0573.62086

Jürgens, U.

Stat. Hefte 26, 237-249 (1985).

Let \(x_ k=(\theta +b_ k)x_{k-1}+\epsilon_ k\), where \(\theta\) is a constant and \((b_ k)\), \((\epsilon_ k)\) are independent sequences of random variables with zero mean, independent also of each other. Then \((x_ k)\) is a random coefficient AR(1) process.
The author proves strong consistency and asymptotic normality of estimators of parameters of the process \((x_ k)\) under conditions which concern only some moments. The proofs are based on martingale differences and they do not need the usual assumptions of strict stationarity and ergodicity.

Reviewer: J.Anděl

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12	Asymptotic properties of parametric estimators

Keywords:

moment conditions; random coefficient autoregressive models; strong consistency; asymptotic normality; martingale differences